ph & pOH - Autoionization of Water

Question

So I was learning about pH and pOH and it made sense. I looked at strong, weak acids & bases and learned that they dissociate completely in water. So then I moved on to water and learned about the autoionization of $\ce{H2O}$.

Here is the process:

$$\ce{H2O + H2O -> H3O+ +OH-}$$

So then I learned about the equilibrium constant and then I figured this: $$\ce{{[H3O+][OH-]} = 1E -14}$$

What does this mean?

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So after that I was doing some basic pH and pOH calculations withe strong acids and bases.

Here is one of them:

Find the pOH of a $\ce{1E-6M} \ce{HCL}$ So here are the steps:

$$\ce{-log[1E-6M] = 6}$$ Ok so the solution had the pH of 6

At first I was like that's nice and I proceeded.

$$\ce{6+pOH=14}$$ $$\ce{pOH=8}$$

So then I was like wait a minute where did the $\ce{OH-}$ come from if it dissociates like this:

$$\ce{HCl + H2O -> H3O+ + Cl-}$$

So then I thought about it and this is what I came up with:

Since there is some $\ce{OH-}$ then there must be some water more water that autoionized into OH and that is the only place where $\ce{OH-}$ could've come from. So that means that even though $\ce{HCl}$ completely dissociated there must be more water than $\ce{HCl}$, because referring to the original equation there is $\ce{1M}$ quantities of $\ce{H2O}$ and $\ce{HCl}$ and so in the $molarity$ of the $\ce{HCl}$ given that means there was more water and less $\ce{HCl}$ and the $\ce{OH-}$ could've only come from the autoionization of that excess water.

So that is what I thought could be the only possible explanation of the $\ce{OH-}$ in a strong acid. And that could only come from $\ce{H2O}$ .

So am I right, and If I am wrong then please tell me where the $\ce{OH-}$ came from.

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Why is the $\ce{pH}$ scale only to $14$? Because if I took a $\ce{2M}$ $\ce{HCl}$ and then I get a super acid in which the $\ce{H+}$ ions is a lot more than the $\ce{H2O}$ available to absorb them. So why is it only to $14$? Does it have to relate to the original autoionization of $\ce{H2O}$?

And If I totally grasped this wrong then can you please accurately tell me what $\ce{pH}$ & $\ce{pOH}$ and what autoionization of $\ce{H2O}$ is for a beginner and still make sense.

Answer 1

I think you have it all right. The OH- present must come from the autolysis of the water present, which is far in excess of the HCl. If you figure the pOH of pure water would be 7, then it makes sense to think that adding 1E-06 M (a small concentration) of HCl would lower the basicity (raise the pOH from 7 to 8).

The reason a scale of 0-14 is used for pH is that when you get to either extreme end of the scale (close to 1M in either acid or base), the sheer concentration of ions present, relative to water, is a game changer and the system no longer behaves in a nice linear fashion. So the scale does not work well outside the 0-14 range. Conceptually, you can extend the pH scale down below zero using concentrated mineral acids or strong acids like fluorosulfonic acid, and empirically measure their effectiveness in protonating a very weak base as a proxy for pH.